Carl, Xavier and Paul have some pens. The ratios of their pens are as follows:
Carl : (Carl + Xavier + Paul) = 1 : 4
Xavier : (Carl + Paul) = 1 : 4
Paul has 77 pens more than Xavier. In the end, Paul gives away all he has to Xavier and Carl so that both Xavier and Carl end up with the same number of pens, how many pens has Carl received from Paul?
Xavier |
Paul |
Carl |
Total |
3x5 |
1x5 |
4x5 |
1x4 |
4x4 |
5x4 |
4 u |
11 u |
5 u |
20 u |
The total number of pens is repeated. Make the total number of pens the same. LCM of 4 and 5 is 20.
Number of pens that Paul has more than Xavier
= 11 u - 4 u
= 7 u
7 u = 77
1 u = 77 ÷ 7 = 11
|
Xavier |
Paul |
Carl |
Before |
4 u |
11 u |
5 u |
Change |
+ 6 u |
- 11 u |
+ 5 u |
After |
10 u |
0 u |
10 u |
Number of pens that Carl has received from Paul
= 10 u - 5 u
= 5 u
= 5 x 11
= 55
Answer(s): 55